Structural and thermodynamic peculiarities of the boundary layers of liquids

STRUCTUlULllDDlSBRHODYl?~C FmuLIAR1!cIBs0P~BOmDARP LUERSOFLIQUIXS B.V.Derjagu3.n Institute of Physical Chemistry of the Academy of Sclenoea 0f the mm, 31, ma13kii Pr08pect, ~00~0~ 117312, u s s R

Gibbs' theory

of oapillaritj,whose centenary anniVer8ary

of publicati-

on haa recently been celebratedat the Leningrad Sympoeium, contemplate6the eurfaoe sone8 at the interface as pos8eaeingproperties that are different from those of phaeee in bulk.In that case, however, a question is left to be anauered as;50 how the properties

Inaide those !#oneB are distributedand

what 58 their tbiakneee.!Chue,Gibbs followers had to solve the problem of providing the specific contenta for the general

thermodmamic

At first, the peculiaritieeand effects have been considered,that are not attributableto the changes in the etrwtuce of liquid (or solvent) as caused by the interface. In the firat place, these comprise the effects depending on the surface field8 of the Van der Waale origin and their overlapping (Lifahite'theory), and the effect8 depending on diffuse ionic atmospheresand their overlapping. It would be advisable to interprete those effects quantitativelyfor the Case of plane-parallelinterlayersa8 two componentsof disjoining presmre. In the case of lyophobic syeteme, it is the taking into account of those Go componentsthat allowed the consecutive theory of stability of lyophobic oolleide to be develeped 1 . Iu epite of the faot that this theory hae been developi.ng already during 42 year6, there remains much to be supplemented. One of the main questions consists in finding correct boundary conditionc~ in integrating Poi#aon-Boltsmonngsequation. It is umaally aesumed that the potential is constant at i&e boundaries of a diffuse ionic layer. This condition ie acceptable 80 far ae the interlayer thickneee is of the order of ionic atmoophereeor thicker. It ie just this thicknees that correspond8to the feroe or potential barrier lf the interactionof partlolee.So, this 355

9. V. Derjaguin juetifies

using

the

asmlnption of the potential constancy in the theory of

stability of lyophobic colloids and in calculating the far potential pit. The eituation,

however, chaqes

for the opposite case of au interlayer that

is much thinner thau the Debyelength.

This we have to deal with in the case

of secondary black free or emulsion film,

or at such aggregation state of

colloidal particles, when the liquid interlayer between them remain8 even after the overcoming of the petential barrier. Certain autho8 2 explain its existence and the peaeibility of it8 subsequent peptization in the following uauuer: at a rapid approach of particles to one another, the adsorption equilibrium ha8 net time to chauge, ewiug to which the last step of approach OCCuPs at COnStaut Charge8 Of SurfaCeS. It is their rather slow relaxation that is able to explain the inpO88ibiliQ

of peptisation after the lengthy

aggregation state. This explanation, however, i8 inapplicable to the etability

of secondary black filus, which 8OBleti1148 psrSiSt8 for year6 and ariSe

al8o at the

slew thW;out

of primaryfilm8.Another

is possible, which should be suitable for interpreting

appreach,however, the stability of any

ultrathin interlayers. In this approach, the mechanior Of charging Surfaces is used as the basis, which allows the surface charge to be calculated in a substantiated way as a function of the interlayer thiclmess. We limit ourselves to the simple case of a diluted 8OlutiOn Containing only one ion-active tenSide, as for example, auion-active eodium oleate. In the aa8e of a sufficiently small thickness of the 8olution interlsyer,which i6 much 8maller than that of the ionic atmesphere, its content of free anions may be neglected. All the auions will be found in adserbed monolayers at the interlayer surfaoes owing te specific adsorption. Part of anions will be blacked by cations, and only the remainingpartof unit area, G

the first determines

the charge of the surface6 per

.

In view of the condition of eleotriaal neutrality, this charge ie compensated for by the charge of cation8 that are present in the film volmt ,,J&dx, where

C(x) is

-h the concentration of oations at a distance of X

symmetry plsne of the film, /t is itu half=thiGkWSS thickness of an ads&tion

(1) from the

(en subtracting the

nonelayer). The adeorption i8etherm will be de-

termined by writing the condition of detailed equilibrium between the proces8es of adrrorption and dosorption

of oatienm

357

SelectedWorkse-c,

=

k (G-CT) ,

(2)

where c,is the concentrationof cations directly close to adsorptionmonolayers; 6,is the charge of surfaces when the adsorbed cations are absent, 80 that difference (Cc- G)is proportionalte the number of the cations adsorbed; & Is the equilibriumconstant. The left side of Equation (2) Is proportionaltc the adsorptionrate, because e

Is proportionalte the num-

ber of "vacant places", which is determinableby the number of anions that are "not blocked" by cations. Instead of Equation (2). we nay writer

Poisson-Boltamam'8 Bquation givest

x2=-Tec,y

(4)

where It,is the potential, E IS the permittivitj;@= Boltzmann constant,T

is the Kelvin temperature, C,

kT

where

k ia the

is the concentration

of cations in the bulk phase, with which the Interlayeris In contact or In the full thermodynamic

equilibrium (in the case of an isolated film).Using

Boltzmaunlsequation,

It will be possible to convert the integral of Equation (4) to:

2% Es

$

= c,-

(6)

c,=

WheN,

(7) designates some length which may be much smaller than d , i.e. the thickness of ionic atmspheres in the solution bulk, if c,- the concentrationof CatiOna

in the eyrmetry

plane of the film

is much higher thsn &., : thie

is realieed at sufficientlysmall values of h_ . For further simplification,we shall examine limit cases of fmall and great thickne8se6.Vhen

,

L< then+

1

(8)

naj be replaced by its argument, snd after carrying out rather s simple calculations,we find:

8. V. Derjaguin

358

As the interlaJerthickness h decreases, the values of CO and

C, > c,

Increase.Let us first consider the case, when c, and CO still remain much smaller thsn g\ , which has a great value. In this case, we obtain from Zquation (3):

In such a case, we derive from Equation (9)t

26,

c

*=zz

(10) l

As Is knem, according to Langmulr 3 , the electrostaticcomponent of disjoining pressure, /7= , is equal to:

(11) Hence, taking into account that for suf+flciently smell values of k

co,> c,,

(12) (13)

ma

is jet not a limit law. At still smaller values of h. , the concentra-

tion of C, will be inoreased to such an extent that the Inverse condition will be reallsedt

c, >> g and similtaueouslj c,*

c,.

(14)

Then from Equations (3) and (9). we deriver

(15)

(16) (17)

We shall have enother limit case, when the taugent argument in formula (6) vi11 tend to 9

, cud when accordiugl~ C,L;< C,. Supposing,however,

that Oondltion C,>>c,is I,=&& Consequently:

preserved,we obtains

359

SelectedWorks- 1

Xormula (21)

coincides

with Langnuir*s

formula

that has been

the case where k is substantially

smsller thau the thicknsss

mospheres, while the dimensionless

potential

than unitJ, which coincides

with conditions

of Equation (12) consists

culiaritJ meters G,

of Sonic at-

of surfaces

is much greater

(18) snd (19).

An essential

in that 0,

depends on adsorption

pepara-

and & . Go , its

As regards

range. It will

value is within a narrow range, when the monolay-

be the higher,

and ths cations

The value of & msy vary within a wide

to saturation.

er is dense and close

respect,

derived for

the easier

the adsorbed molecules dissociate

pass over from the monolayer into ths film bulk. In this

lithium and sodium ions occupy the first

ens, both kinds of ions exhibiting

an increased

, the following

place in aqueous aolutihydration energy. On having

assessed possible

values of

&

csn be established

ple calculations:

transition

with a deorease in /L from formula (21) to

formulas (13) and (17) Is accompanied by a drastic magnitude) Increase

In n,

in fle with a decrease in really

smsll values of

ct

. The reverse - odng

(by several orders of to a more drastic

in formula (21) - can be attained

k

(less

by sim-

than loo9 cm).

increase

only at un-

lie would achieve still

higher values in the ease when the charge should remain constant as the thiclmess of 1, diminishes. um conditions;

therefore,

the lengthy stability

films oannot be attributed Bar

evaluating

expression

nIk, the

(17) for

fI,

where b,

of,

for example, black soap

to that circumstance.

the stabllising

role

of n,

in “8uperthizP

films,

will have to be compared with the expression

molecular component of disjoining

n I

However, this is Incompatible with the equilibrin

for

which is equal to

A

m=q-

Is the effective

pressure,

the

thiclmess

(22)

J of the film,

exceeding

of the same order of magnitude with it 4 . At values

A

h

but being

of the order of

B. V. Derjaguin

360 10-Q

to 10-13,

at L %10-g

and at possible

cm n,

tensides

considered

Of course, order

of

the

of

the structure

adsorbed

ions

their

attraction.

that

the normally

of

“black

it

films”

Our calculations where the surface surface

of

motic

character

of Martinov layers

the behaviour

attention

case,

for

to their

with

the separation

example,

is

is

of

thiclmess

sre

were strongly

a slight trical

permeable

sta-

also,

0

functlthe

in

mobility, neutrality.

the liquid us consider

ion-active,

for

In other

be able

of

the section

in the

SOlUtiOn

interlayer, the case

of

the formation

the contrary

is

to

the Wis-

zones

only

the flow

con-

In view will

over-

solution.

counterions

would infringe

for

that

be separated.

a dense monolayer

of

obvious:

quite of

the

msy be

a pore which,

drop of potential.

the solution

of

osz~sis

of an electrolyte

counterions

the os-

the molecules

the surface

of

not

and inasmuch

The ions

tc purify

osmosisa

The following

bulk.

words,

of “reverse

the capillary

as we have seen,

of

problem

are used,

all

then,

and the flow

the appearance

the membrsne will

there

has attract-

and biological

by how the concentration

across

from that

in the interlayer

would cause

7

interlsyers

we assume to be slit-shaped,

of let

determined

distributed

different

of all,

be present

is

simplicity,

centration

it

C,

in the process

denomination,

but such that

effect

solvedW component

First

dis-

of ionogen

the technical

to be separated. In such membranes, 7 observed rather thsn the ordinary osmosis.

lap.

to

calculations.

case

liquid

mixture

a small

close

to the case,

to the limit

of

the long-time

of diesociatlon

of “ultrathin”

in connection

contrary

membranes,

the sake of

that

applicable

and

has been shown

at very

of developed

as a result

This corresponds

6 it

are attracted

in favour

Muller

_and may even lead

snd Gnilga

speaks

k

character

the diatribution

repulsion

not be underestimated

chsrged

the discrete

of

should

the membrane separation,

In that

of

of

calculations.

Recently, ed a great

is

at the values

to become perceptible.

are simultaneously

groups.

aforementioned

when the effect

dipole

by ion-ac-

interlayers

efficient.

electrostatic

In the study

Nonetheless,

bility

tc be very

begins

their

that even

l

the discrete

oriented

has been found

made become8 incorrect

of monolayer6

decreases

& , it

of

of “ultrathin”

a few monolsyers,

5 have shown that

I%Jaguin

tances.

proves

the calculation

on

onal

n,

>

the mechanism of stabilization

Thus, tive

values

If would

possess

on the elecof counterions Therefore,

from such a0 electrolyte.

but

361

Selected Works - 1

Of course, at high filtration rates the purification degree will drop owing to the fact that the entraining aud the carrying away of counterions will be accompsnied by dosorption of adsorbed ions. sow, let us oonsider the flow of a solution of nonelectrolytes through the membrane. The author snd his ooworkers examined the capillary osmosis of solutioas of nonelectrolytes. The existence of the latter in the light of the theor? developed by the author

7 proves

the

diffuse structure of the mo-

vable psrt of au adsorption lajer. Using this as the basis, the separation effect of reverse osmosis will have to be exsmined; it would be more correct to designate it as "reverse capillary osmo8i8". The factor common to both OffeCtS are the moleculsr forces acting upon the molecules dissolved close to the interface. By snalog~ dth

Lifehits' method for deriving the forces

of paired interaction of molecules, the energy of effective attraction of dissolved molecules of a diluted solution to phase surface8 was established in a study dealing with the theoretical aud experimental investigation of oapillarj 088osis 8,

u (h) = -

A

77

(23)

where

(24) where h. is the distance from the interface, ti is the Plsnck constant, is the solution pemaittivitj,

is

the permittlvity

E,

Is

the permlttivity

of the wall, C is

of the solvent,

f, E3

the number of molecules that are dis-

solved in the solution volume uuit. All &; sre taken as a function of imaginary frequency i 5 . Using Boltzmann~sequation, we find the concentration of dissolved molecules in sn interlayer of thiclmess L

by formula:

(25)

In the

case

if

A

is

ptm~tivo,

we hare t

C>C,’ %!hls,

(26)

as was shown by Churaev g , is conducive to the fact that filtration

of a solution through a membrane is accompaniedby a concentrationdrop of

dissolved molecules, which till just be characteristic of its separation eifect.

6. V. Derjaguin

Another importantcorollary of Bquation (25) consiste in that it groves to be impracticableto apply Dsyaloshinskij,Lifshits snd Pitaevsldjformula to the calculationof the disjoiningpressure of au solution interlayer, the formula supposing the uniformityof the interlsyer.This problem was solved by Churaev and me lo by using Gibbs-D&em's equationwhich allowed the disjoiningpressure of the interlayerof nonelectrolytebinary solution to be expressed by formulat fi

n=-

ar (h) ---d/*-4%, -a

(27)

--bo

where r(k) is the excess number of dissolvedmolecules in the system at a given value of the chemical potential of the solute,p, values of pressure 10 aud temperatureT

and the prescribed

, the number of the molecules of

the solvent and the concentrationof dissolved molecules C,

in the solu-

tion bulk, at a distance of plates L as compared with distance A

Wglo,

flI?designates the disjoiningpressure of an interlsyerof the pure solvent at the same thickness L

The value of /7fi csn be accuratelycslculatedby

Lifshits et al'." formula, if, of course, the structuralpeculiaritiesof the solvent close to interfaceswith plates be disregarded.Rormulas (23), (24), (25) and (27) allow calculating n

.

Analysis of the equations derived has shown the followingr the dispersion component of disjoiningpressure may be positive, if eon&ant

A

is

positive and sufficientlygreat (supposingthat the influence of electromsgnetic retardationis not yet essential).!i!his consequenceof our theory is in

qualitativeagreementwith findings of Sheludko and Rkserova I2 relative

to the stability of free films of butyric acid aqueous solutions.It will be of interest to check the developed theory for the case where both eurfaces are unlike, n,,,=0 , and, hence, fl is completelydeterminedby the overlapping of adsorptionatmospheres.In the studies of Kuuy, Rueanov snd Brodskij I3 , the disjoiningpressure of the interlayersof solutionsis interpretedon the basis of taking into account paired interactionssnd without using formulas (24) and (27) derived by us. !Rhisdoes not allow obtaining quantitativeresults, when using macroscopicconstants as the starting point. At present, there has been accumulateda great amouut of experimental data showing that in a number of cases the consideredoomponentsof disjoining pressure are insufficientfor explaining the interactionof phases separatedby thin interlayers.In particular,the interactionarising changes

Selected Works - 1

363

abruptly with the nature of the eurface a8 a reeult -nonactive

tenaides.

the forth

component of disjoining

are overlapped,

There are relevant

whose etrwture

one under the Influence

of the interface.

proved unambiguouely Therefore, carried

featwee

referring

out reoently pressure.

we shall designate

of tbia component ie

owing to the fact

that the theor

ha8

and due to a emall number of studies,

of the boundary layers

to a number of original

br Ninham et al.14, of the existence

!Ehemost direct

of liquids

in

have been

surfaces

result8

we limit

ourselves

of the struotural

to setting

forth

component of dis-

pressure of wetting filme of water on

of quartt,, glaes,

eented the e%perimentd

studies that have been

and unambiguous proof6 were obtained by

examining the isotherm of disjoining hydrophylic

that

.

the experimental proofs joining

Hereinbelow,

one. The erirtence

insuffioientlj,

whiah the structural

to believe

has been changed a6 oompared with the bulk

but with a great delay,

been developed jet

ground8 available

preeeurs appears when the boundary lwers

that component a8 the structural reoognised

of adsorptionof ion-

mica (muecovite),

In Fig.1 are pre-

of various author6 ‘5s’6*‘7

determining /Tfi)

I 12.

Fig. 1. MejoinIng 1. Water

IO’

0 8.10'

peesure

04.104

isothermal for wetting

on mica I5

fi-films /

2. Rater on glaae I5

3. 2.10-5 N aqueous KC1 solution 4.

5.

IO4 N aqueous NaCl solution Water on quarts 16

on quarts

16

on glaee I5

6. Water on quarts I7

for water on auarts and glase

K-8. These data, like the first measurementa made by Derjaguin and Kueakov 15 , were obtained by resorting to a method of Preeeing a gae bubble to a flat

plate,

and of measuring the equilibrium

9. V. Derjaguin

364

thicknessof a netting

film h and the capillarypressure of the bubble,

which correspond to each other. It is obvious that for great thicknessand, accordingly,small values of /J , the experimentalpoints of different authors are located close to a curve that was plotted according to Langmuir I8 equation !=zE

n,=,-

y2

0 c

_e

.

J

(28)

‘J!his equation defines the ionic-electrostatic componentof the disjoining

pressure of a wetting film in the assumption that the substratepotential is very great (~o>lOO mV), the charge of the free surface is equal to zero, while the (dimensionless)

thickness

Xh

4~.

is

smalls

1.

(29)

However, when fl of the wetting film increases and it accordingly grows thinner, it goes beyond the boundary of stability (or rather metastability). In such a case, there occur local breakups, In which there form thinner sections.Eventually,the greater part of the film acquires a smaller stable thickness,while the remaining part of the initial thicker film breaks up into small lenses forming with the thin film the final contact angle of the ordex of 5 to IO*.

The

branch of the isotherm of disjoining

pressure correspondingto thinner wetting films was obtained in a number of studies I9 , by plotting the dependence of the thicknessof polymolecular "adsorbed"films of water on the relative pressure of vapour p/T, beginning with p/f5=f

, where 'pS is the pressure of vapour over the flat surface of

the same liquid in bulk. pig. 2 representson one graph both

sections/of

the /'7(h)isotherm, i.e. that of thicker,b -layers end that of thinner, h, 200

ii

(a)

Fig. 2. L vs

n drdcm*-isotherm for water on glass, 15, 4- film I9 (curve 1); e isotherm (curve 2); L vs flmisotherm(curve 3).

Selected Works- 1

365

d-layers 20 . The lower part of B -section correspondsto the metastable states of a wetting film. A remarkable fact is that & - section of thinner layers of n(h) isotherm intersects the orinate correspondingto the value n=o

at a finite value

h= k,. The values

a Corollary

of

0

a following

0.

*

dh c

(31)

Owing to this condition, anj variation in thicknesswill increase due to an exchangewith the vapour phase. On the same figure, curve 2 represents isothermwhich has been plotted according to equation (28) that gives & the maximum possible limit of n, values within the range of small thicknesses. Curve 3 represents the dispersion component, fl,, which for ll/-=20of

ConstantA

300 A"

satisfiesequation:

, which was

calculatedby B.V.Churaev20 according to E.M.Lif-

ehits et al.* theor on the basis of quartz end water absorptionspectra, has value A=-

Y, 42 . fo-3

ew.

(33)

Thus, it is obvious that the superimpositionof components fl, and n, of disjoiningpressure is not able to give, even approximately,the Isotherm which was observed within the region of d -layers. Moreover, bj this means it is impossible to explain the reversing of the sign of This is an unambiguousproof that d the

StrUCtUrSl

n(h) at A = L,

- branch of the isotherm stems from

peculiaritiesof water layers that are adjacent to the

quartz surface. This is also substantiatedbr the temperaturedependenceof the characteristicthickness A, of d-

layers. The value of /I., decreases

as temperatureis raised, and at to - 70" it is reduced to the monolayer thiclmess21 . That the observed isotherm of disjoining pressure cannot be ascribed to Van der Waals force8 aleo reeulte from the fact that hjdropho-

366

B. V. Derjaguin

bization cular

of glass

1aJers

explained

with a monolayer

lar

to the disappearance

of water under any pressures

on the basis

of

Now, the isotherms -polar

leads

liquids

of water vapour.

the molecular

of

attraction

the disjoining

on some substrates

component of disjoining

pressure,

as en example the isotherm

of

n,

of wetting

identified

. In Rig.3,

the disjoining

This cannot

be

#laws.

pressure

may be fully

of poljmole-

with

there

pressure

films

of non-

the molecu-

is represented

of h -hexane

wetting

- h,ii

(b)

’ 600

- 400

.

I

.

,

400 Fig.

film

3.

n

200 vs

d&cm2

22 . Measurements

on steel

thickness

instead

to plotting

isotherm:

with

6

the film,

limit

case

of water, change

of

distances

= -1.6.10

the full

effect

would be natural

the substrate.

of

of

scores

disturbs

tural

of disjoining

component

structural

the assumption component,

Examination ther

substantiation

of

having

a formula

thickness was applied

(34)

of

and corresponds

erg. cm

electromagnetic

to ascribe

the order kgstrdm.

the s~sten

of for

the structural

of

architecture correlation

disappear influence

is able

the viscosity

of

of

peculiarities.

structural

bonds;

peculiarities

thin

only

layers

of

to a

active

csn be restored

at

length,

which is

higher

than 70%,

therefore,

, too. of

in the

23 . In case

bonds under the effect

of hydrogen

the possible solubility

retardation

At temperatures

pressures

to the interaction

the hind of metal used,

from

Such a disturbed

the heat motion

refutes

-19

of hydrogen

from the surface

on the order

(32),

on steel.

A4

in the architecture

centers

water

it

films

to the films

of formulas

which is independent

of

R-hexane

-0 =-,

“* where constant

of

were limited

more than 400 ii. Therefore, the theoretical

I,“”

.

also

solubility

to grow with of water

the struc-

This fact

quarts

on the

temperature.

serves

An increased

for

as a fur-

ViSCO8itJ

of

367

Selected Works- 1

those layers on the quartz-glassinterfacewas detected on observingwhether the flow of rater in quartz capillaries24 up to 200 i in radius, or the flow of thin water films wetting glass and quartz 25 . In layers about 50 i thick, at a temperatureof about 20°C there is observed an increase in

ViS-

cosity by several times as compared with the bulk value. It is remarkable that this increase in viscosity disappearsat the same temperatureof 70°C, at which the structuralcomponent of disjoiningpressure disappears. Finally, the structuralpeculiaritiesof boundary layers of water were independentlyproved by examining thermoosmosiswhich was detected in 1947. This phenomenonconsists in the flow of liquid through glass capillariesor 26 . In accordance diaphragmpores under the effect of a temperaturegradient with Derjaguin'stheory 26 based on using thermodynamicsof irreversible processes, the thermoosmoticflow rate

through a capillaryhaving the dt form of a slit with thickness h is equal to:

(35) where

h/z d //(x)x(h-xld3: X"

J

"J)

9

(36) 0 where a/f is the excess of the enthalpy density as compared with the bulk is viscosity,X is the coordinatewhich is read off one surface of value 9‘3 the slit. It is supposed that the width of the capillary is much greater than the width of leyers in which the specific enthalpy is different from the bulk value. Part of the change in the enthalpy may be ascribed to the effect of ionic atmospheresthat form close to the slit surfaces.For water, this part is small, as follows, firstly, from an insignificantinfluence of the electrolyte concentration,and secondly,from the fact that thermoosmosisintensity which decreases as temperatureincreases,disappears at a temperature of 7ow 27 . Peculiar is the dependenceof the thermoosmoticflow on the capillary radius (see Fig.4). At great radii (on the order of 1 ,um>, the thermcosmoticflow is directed towards the increasing temperature,and its flow rate is comparativelysmall. As the capillary radius (see Pig.4) decreases below 500 1, the direction of the .thermoosmotic flow changes to the directly opposite one, i.e. in the direction of decreasing temperature,and, what is the most

surprising,

it

increaseswith a further decrease in the ra-

dius. The change in the direction of thermooamosisto the directly opposite

368

B. V. Derjaguin L_

__I_.._

10

100x -_

100

1%

I~

1

t=200c

! !

I.grad T=200”cm-I 2gradT=250°cm-1

2

2 I 01 -2L-L

I

1

_.__-.

_-

5

10 Lni

Fig.

4.

Thermoosmosis

one with

the layer

of water

consists

and for

fluence

of

one another

Zt

flow 15

ctional

appearance face

(for

bodies

component

mentioned

the change

-ionogen

surfactants

example,

polyglycol

adsorption.

study

an adjacent

pressure

centers

or radii

layers

overlap

hydrosol

layers.

of

of

there able

iodide

additions

of

is

chains

the

the sur-

of

appears

the

to guarantee

silver

the valence

fun-

can be modified

there into

the

may be lyophilic

concentrated

so-

the counterion).

achieved

medium, the surfactants

oxaethyl

active

Hence,

As an example, of

of

that determines

which is

2g that modification

having

h

in the thermo-

phase,

particles)

system.

to the aqueous

the in-

such a change in

an increase

As a result,

under the effect

esters

Without

colloid

colloid

capillaries,

un-

themselves. of

lyophobic

(independently

to Glazman’s

to explain

is positive,

thicknesses

them changes.

layer

to indicate

as the boundary

(or

of lyophobic

of electrolytes

for

narrow

of disjoining

only

of

of boundary

a corresponding

coagulates

radii

peculiarities

of monolayer

of

According

each of

impossible

at smaller

OH) and charged

example,

stability

lutions

prevails;

on the surface

structural

under the effect

one that

of

whereas

the boundary

one of which AH

is

h or

would be impossible

of lyophobic

structural

layer

for it

thicknesses

Is greater,

the presence

of

that

two layers,

as the capillaries

groups

unambiguously

negative

another

it

raaaus.

of

the structure

the structure,

proves

capillary

28 . However,

one layer of

vs

at least

why at greater

the influence

osmotic

thickness

the other

ambiguously

rate

of different

by adding being,

for

lengths.

non

Selected Works-

369

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